Numerical continuation techniques for planar slow-fast systems

Abstract : Continuation techniques have been known to successfully describe bifurcation diagrams appearing in slow-fast systems with more than one slow variable (see, e.g., [M. Desroches, B. Krauskopf, and H. M. Osinga, Nonlinearity, 23 (2010), pp. 739--765]). In this paper we investigate the usefulness of numerical continuation techniques dealing with some solved and some open problems in the study of planar singular perturbations. More precisely, we first verify known theoretical results (thereby showing the reliability of this numerical tool) on the appearance of multiple limit cycles of relaxation-oscillation type and on the existence of multiple critical periods in well-chosen annuli of slow-fast periodic orbits in the plane. We then apply the technique to study the period function in detail.
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Article dans une revue
SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2013, 12 (3), pp.1159-1180. 〈http://epubs.siam.org/doi/abs/10.1137/120877386〉. 〈10.1137/120877386〉
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Contributeur : Mathieu Desroches <>
Soumis le : lundi 15 juillet 2013 - 22:01:46
Dernière modification le : vendredi 25 mai 2018 - 12:02:05

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Peter De Maesschalck, Mathieu Desroches. Numerical continuation techniques for planar slow-fast systems. SIAM Journal on Applied Dynamical Systems, Society for Industrial and Applied Mathematics, 2013, 12 (3), pp.1159-1180. 〈http://epubs.siam.org/doi/abs/10.1137/120877386〉. 〈10.1137/120877386〉. 〈hal-00844785〉

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